{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Orthogonal polynomials"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {},
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as pt"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Mini-Introduction to `sympy`"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {},
      "outputs": [],
      "source": [
        "import sympy as sym\n",
        "\n",
        "# Enable \"pretty-printing\" in IPython\n",
        "sym.init_printing()"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Make a new `Symbol` and work with it:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$\\left(x^{2} - 3\\right)^{2}$$"
            ],
            "text/plain": [
              "        2\n",
              "\u239b 2    \u239e \n",
              "\u239dx  - 3\u23a0 "
            ]
          },
          "execution_count": 4,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "x = sym.Symbol(\"x\")\n",
        "\n",
        "myexpr = (x**2-3)**2\n",
        "myexpr"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$x^{4} - 6 x^{2} + 9$$"
            ],
            "text/plain": [
              " 4      2    \n",
              "x  - 6\u22c5x  + 9"
            ]
          },
          "execution_count": 5,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "myexpr = (x**2-3)**2\n",
        "myexpr\n",
        "myexpr.expand()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$\\frac{x^{5}}{5} - 2 x^{3} + 9 x$$"
            ],
            "text/plain": [
              " 5             \n",
              "x       3      \n",
              "\u2500\u2500 - 2\u22c5x  + 9\u22c5x\n",
              "5              "
            ]
          },
          "execution_count": 6,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sym.integrate(myexpr, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$\\frac{72}{5}$$"
            ],
            "text/plain": [
              "72/5"
            ]
          },
          "execution_count": 7,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "sym.integrate(myexpr, (x, -1, 1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "## Orthogonal polynomials"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Now write a function `inner_product(f, g)`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {},
      "outputs": [],
      "source": [
        "def inner_product(f, g):\n",
        "    return sym.integrate(f*g, (x, -1, 1))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Show that it works:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA0AAAASCAYAAACAa1QyAAAABHNCSVQICAgIfAhkiAAAAMJJREFUKJHF0j9LQlEYB+DH6BNYhJ/HxcmpD9CgQ0OImxAIbi5u7eLSJji5NzQGDRItDtHQ3J0aSnS4LxJytBMN/eBw4XCe+77nD3/MCdqYYYkPFLhHC0cpdIk13nCLIcZ4j/kpKruojmbijzW8Bjz/TevXgW7s6zORz/h+5VY5xiIqNXLRKMA8F3QCPKOaA64CPClP8Md0AyxwlgN6AR5xmgP6AR4c2MP3Z3GBCVbKSywS619izTaDqHJo3OW0+8/ZALIVMPhgrAZWAAAAAElFTkSuQmCC\n",
            "text/latex": [
              "$$2$$"
            ],
            "text/plain": [
              "2"
            ]
          },
          "execution_count": 9,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "inner_product(1, 1)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAA4AAAASCAYAAABrXO8xAAAABHNCSVQICAgIfAhkiAAAAMRJREFUOI3N0r1OgkEQheEnlhqDxlYrA9wCLRfkdWhlLK30FmixsOMe+CnQRmOnUQstxGa+8GVgCRgLpjnZs/PuZHcP/1jHuMETvvCAKxyugk7xghl6uMB9rIc4KoH9aDpL/mX416VpM0yxk/b28YFP7EkN3dA7/CTwHQPsopPBdui4cI1JaCuDjdC3Alj5BxncqOpgdWJjWWPNf83gKLRVAJuhC2+w0Xfk+lMAqqn1yJ2bR25kReTgBLd4xjcerRHyLa5fD28wqzSkqLgAAAAASUVORK5CYII=\n",
            "text/latex": [
              "$$0$$"
            ],
            "text/plain": [
              "0"
            ]
          },
          "execution_count": 10,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "inner_product(1, x)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Next, define a `basis` consisting of a few monomials:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 44,
      "metadata": {},
      "outputs": [],
      "source": [
        "basis = [1, x, x**2, x**3]\n",
        "#basis = [1, x, x**2, x**3, x**4, x**5]"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "And run Gram-Schmidt on it:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 45,
      "metadata": {},
      "outputs": [],
      "source": [
        "orth_basis = []\n",
        "\n",
        "for q in basis:\n",
        "    for prev_q in orth_basis:\n",
        "        q = q - inner_product(prev_q, q)*prev_q / inner_product(prev_q,prev_q)\n",
        "    orth_basis.append(q)\n",
        "\n",
        "legendre_basis = [orth_basis[0],]\n",
        "\n",
        "#to compute Legendre polynomials need to normalize so that q(1)=1 rather than ||q||=1\n",
        "for q in orth_basis[1:]:\n",
        "    q = q / q.subs(x,1)\n",
        "    legendre_basis.append(q)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 46,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$\\left [ 1, \\quad x, \\quad \\frac{3 x^{2}}{2} - \\frac{1}{2}, \\quad \\frac{5 x^{3}}{2} - \\frac{3 x}{2}, \\quad \\frac{35 x^{4}}{8} - \\frac{15 x^{2}}{4} + \\frac{3}{8}, \\quad \\frac{63 x^{5}}{8} - \\frac{35 x^{3}}{4} + \\frac{15 x}{8}\\right ]$$"
            ],
            "text/plain": [
              "\u23a1         2         3            4       2          5       3       \u23a4\n",
              "\u23a2      3\u22c5x    1  5\u22c5x    3\u22c5x  35\u22c5x    15\u22c5x    3  63\u22c5x    35\u22c5x    15\u22c5x\u23a5\n",
              "\u23a21, x, \u2500\u2500\u2500\u2500 - \u2500, \u2500\u2500\u2500\u2500 - \u2500\u2500\u2500, \u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500 + \u2500, \u2500\u2500\u2500\u2500\u2500 - \u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u23a5\n",
              "\u23a3       2     2   2      2     8       4     8    8       4      8  \u23a6"
            ]
          },
          "execution_count": 46,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "legendre_basis"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "These are called the *Legendre polynomials*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "--------------------\n",
        "What do they look like?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 47,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 576x576 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "mesh = np.linspace(-1, 1, 100)\n",
        "\n",
        "pt.figure(figsize=(8,8))\n",
        "for f in legendre_basis:\n",
        "    f = sym.lambdify(x, f)\n",
        "    pt.plot(mesh, [f(xi) for xi in mesh])"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "-----\n",
        "These functions are important enough to be included in `scipy.special` as `eval_legendre`:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 48,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import scipy.special as sps\n",
        "\n",
        "for i in range(10):\n",
        "    pt.plot(mesh, sps.eval_legendre(i, mesh))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "What can we find out about the conditioning of the generalized Vandermonde matrix for Legendre polynomials?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 49,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$7274.598185486346$$"
            ],
            "text/plain": [
              "7274.598185486346"
            ]
          },
          "execution_count": 49,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#keep\n",
        "n = 20\n",
        "xs = np.linspace(-1, 1, n)\n",
        "V = np.array([\n",
        "    sps.eval_legendre(i, xs)\n",
        "    for i in range(n)\n",
        "]).T\n",
        "\n",
        "la.cond(V)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "The Chebyshev basis can similarly be defined by Gram-Schmidt, but now with respect to a different inner-product weight function,\n",
        "$$w(x) = 1/\\sqrt{1-x^2}.$$"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 50,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$\\left [ 1, \\quad x, \\quad 2 x^{2} - 1, \\quad 4 x^{3} - 3 x, \\quad 8 x^{4} - 8 x^{2} + 1, \\quad 16 x^{5} - 20 x^{3} + 5 x\\right ]$$"
            ],
            "text/plain": [
              "\u23a1         2         3           4      2          5       3      \u23a4\n",
              "\u23a31, x, 2\u22c5x  - 1, 4\u22c5x  - 3\u22c5x, 8\u22c5x  - 8\u22c5x  + 1, 16\u22c5x  - 20\u22c5x  + 5\u22c5x\u23a6"
            ]
          },
          "execution_count": 50,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "w = 1 / sym.sqrt(1-x**2)\n",
        "def cheb_inner_product(f, g):\n",
        "    return sym.integrate(w*f*g, (x, -1, 1))\n",
        "\n",
        "orth_basis = []\n",
        "\n",
        "for q in basis:\n",
        "    for prev_q in orth_basis:\n",
        "        q = q - cheb_inner_product(prev_q, q)*prev_q / cheb_inner_product(prev_q,prev_q)\n",
        "    orth_basis.append(q)\n",
        "\n",
        "cheb_basis = [1,]\n",
        "\n",
        "#to compute Legendre polynomials need to normalize so that q(1)=1 rather than ||q||=1\n",
        "for q in orth_basis[1:]:\n",
        "    q = q / q.subs(x,1)\n",
        "    cheb_basis.append(q)\n",
        "cheb_basis"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 51,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "for i in range(10):\n",
        "    pt.plot(mesh, np.cos(i*np.arccos(mesh)))"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Chebyshev polynomials achieve similar good, but imperfect conditioning on a uniform grid (but perfect conditioning on a grid of Chebyshev nodes)."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 52,
      "metadata": {},
      "outputs": [
        {
          "data": {
            "image/png": "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\n",
            "text/latex": [
              "$$4846.7105682362735$$"
            ],
            "text/plain": [
              "4846.7105682362735"
            ]
          },
          "execution_count": 52,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "#keep\n",
        "n = 20\n",
        "xs = np.linspace(-1, 1, n)\n",
        "V = np.array([\n",
        "    np.cos(i*np.arccos(xs))\n",
        "    for i in range(n)\n",
        "]).T\n",
        "\n",
        "la.cond(V)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.5.2"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 1
}